Nonresponse in panel studies can lead to a substantial loss in data quality due to its potential to introduce bias and distort survey estimates. Recent work investigates the usage of machine learning to predict nonresponse in advance, such that predicted nonresponse propensities can be used to inform the data collection process. However, predicting nonresponse in panel studies requires accounting for the longitudinal data structure in terms of model building, tuning, and evaluation. This study proposes a longitudinal framework for predicting nonresponse with machine learning and multiple panel waves and illustrates its application. With respect to model building, this approach utilizes information from multiple waves by introducing features that aggregate previous (non)response patterns. Concerning model tuning and evaluation, temporal cross-validation is employed by iterating through pairs of panel waves such that the training and test sets move in time. Implementing this approach with data from a German probability-based mixed-mode panel shows that aggregating information over multiple panel waves can be used to build prediction models with competitive and robust performance over all test waves.